Fisher information and the central limit theorem
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Publication:2249581
DOI10.1007/s00440-013-0500-5zbMath1372.60018arXiv1204.6650OpenAlexW2123901758MaRDI QIDQ2249581
Sergey G. Bobkov, Friedrich Götze, Gennadiy P. Chistyakov
Publication date: 2 July 2014
Published in: Probability Theory and Related Fields (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1204.6650
Related Items (16)
On the time-dependent Fisher information of a density function ⋮ The fractional Fisher information and the central limit theorem for stable laws ⋮ Score functions, generalized relative Fisher information and applications ⋮ Local Limit Theorems for Smoothed Bernoulli and Other Convolutions ⋮ Poincaré-type inequalities for stable densities ⋮ Central limit theorem in uniform metrics for generalized Kac equations ⋮ Entropic isoperimetric inequalities ⋮ Approximation of Markov semigroups in total variation distance under an irregular setting: an application to the CIR process ⋮ Higher-order Stein kernels for Gaussian approximation ⋮ Rényi divergence and the central limit theorem ⋮ Entropy inequalities for stable densities and strengthened central limit theorems ⋮ Regularity of linear and polynomial images of Skorohod differentiable measures ⋮ Convergence and asymptotic approximations to universal distributions in probability ⋮ Upper bounds for Fisher information ⋮ Stein's method, logarithmic Sobolev and transport inequalities ⋮ An invariance principle under the total variation distance
Cites Work
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- Large deviations and isoperimetry over convex probability measures with heavy tails
- Some inequalities satisfied by the quantities of information of Fisher and Shannon
- Solution of Shannon’s problem on the monotonicity of entropy
- The convolution inequality for entropy powers
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